I believe you're understanding it rightly. If, for example, your motor runs at 1500rpm, you can convert that to Hz. 60rpm = 1Hz. So your motor is running at 25Hz. If there was any imbalance in your motor (e.g. a shaft isn't quite perfectly round) it will probably put a small force on your weldment 25 times every second. In other words, there would be a vibration input at 25Hz.
So if your weldment has a natural frequency of 25Hz, it will want to dance right along with the motor's input vibration. Eventually, the vibations displacement will add up and add up and you'll have catastrophic failure of your weldment. So you want your frame weldment to have a natural frequency about 2 times above 25Hz (in this example) so that when the motor is running at its fastest, it won't wreck the frame.
If your machine base's natural frequency is less than that of the motor, that means that while the motor is getting up to speed, it will pass through the resonance range of your machine base, causing a lot of excessive vibration. Some machines have this problem and there's nothing to be done about it but have a strategy to pass through the resonance zone in the safest possible way. You'd want to avoid this if you can.